1. Divisibility and Mental Math

2. Vocabulary A number is divisible by another number if it can be divided into and result in a remainder of 0. 24 is divisible by 4, because 24 ÷ 4 = 6. 24 is not divisible by 5, because 24 ÷ 5 = 4.8 (or 4R4). An even number ends with a 0, 2, 4, 6, or 8. An odd number ends with a 1, 3, 5, 7, or 9.

3. Divisibility Rules 2 divides into all even numbers. 3 divides into a number if the sum of the digits of that number is divisible by 3. 4 divides into numbers where the last two digits are divisible by 4. 5 divides into numbers that end with a 5 or 0.

4. 10 divides into numbers that end with 0. Divisibility Rules (continued) 6 divides into a number if it is divisible by both 2 and 3. 9 divides into a number if the sum of the digits of that number is divisible by 9.

5. Example: Test each number for divisibility by 3. 216 2 + 1 + 6 = 9 9 is divisible by 3, so 216 is divisible by 3. yes 437 4 + 3 + 7 = 14 14 is not divisible by 3, so 437 is not divisible by 3. no

6. Example: Test the number for divisibility by 2, 5, or 10. 454,320 2 works because the number is even. 5 works because the number ends with 0. 10 works because the number ends with 0. Is the number divisible by 9? 4 + 5 + 4 + 3 + 2 + 0 = 18. 18 is divisible by 9, so 454,320 is also divisible by 9.

7. Example: Test the number for divisibility by 4 216 16 ÷ 4 = 4 16 is divisible by 4, so 216 is divisible by 4. yes

8. Example: Test the number for divisibility by 6 210 2 works because the number is even. 2 + 1 + 0 = 3 3 is divisible by 3, so 210 is divisible by 3. Because 2 & 3 both work…… then 6 automatically works. 436 2 works because the number is even. 4 + 3 + 6 = 13 13 is not divisible by 3, so 436 is not divisible by 3. Since 3 doesn’t work, then 6 can’t work. no yes

9. Homework Time